Unconventional Josephson effect in hybrid superconductor-topological insulator devices

Topological band inversion and chiral Majorana mode in hcp thallium

The chiral Majorana fermion is an exotic particle that is its own antiparticle. It can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM. Thekz=0plane of Tl is a mirror plane, realizing a full-gap band inversion corresponding to a topological crystalline insulating phase. Its surface and hinge are stable and easy to make various structures. Another notable feature is that the surface Dirac point is very close to the Fermi level, so that a small Zeeman field can induce a topological transition. Our calculation indicates that Tl will provide a new platform of the Majorana fermion.

Contribution of Processes in SN Electrodes to the Transport Properties of SN-N-NS Josephson Junctions

In this paper, we present a theoretical study of electronic transport in planar Josephson Superconductor-Normal Metal-Superconductor (SN-N-NS) bridges with arbitrary transparency of the SN interfaces. We formulate and solve the two-dimensional problem of finding the spatial distribution of the supercurrent in the SN electrodes. This allows us to determine the scale of the weak coupling region in the SN-N-NS bridges, i.e., to describe this structure as a serial connection between the Josephson contact and the linear inductance of the current-carrying electrodes. We show that the presence of a two-dimensional spatial current distribution in the SN electrodes leads to a modification of the current-phase relation and the critical current magnitude of the bridges. In particular, the critical current decreases as the overlap area of the SN parts of the electrodes decreases. We show that this is accompanied by a transformation of the SN-N-NS structure from an SNS-type weak link to a double-barrier SINIS contact. In addition, we find the range of interface transparency in order to optimise device performance. The features we have discovered should have a significant impact on the operation of small-scale superconducting electronic devices, and should be taken into account in their design.

Proximity-induced superconductivity in epitaxial topological insulator/graphene/gallium heterostructures

The introduction of superconductivity to the Dirac surface states of a topological insulator leads to a topological superconductor, which may support topological quantum computing through Majorana zero modes^1,2. The development of a scalable material platform is key to the realization of topological quantum computing^3,4. Here we report on the growth and properties of high-quality (Bi,Sb)₂Te₃/graphene/gallium heterostructures. Our synthetic approach enables atomically sharp layers at both hetero-interfaces, which in turn promotes proximity-induced superconductivity that originates in the gallium film. A lithography-free, van der Waals tunnel junction is developed to perform transport tunnelling spectroscopy. We find a robust, proximity-induced superconducting gap formed in the Dirac surface states in 5-10 quintuple-layer (Bi,Sb)₂Te₃/graphene/gallium heterostructures. The presence of a single Abrikosov vortex, where the Majorana zero modes are expected to reside, manifests in discrete conductance changes. The present material platform opens up opportunities for understanding and harnessing the application potential of topological superconductivity.

Selective Area Epitaxy of Quasi-1-Dimensional Topological Nanostructures and Networks

Quasi-one-dimensional (1D) topological insulators hold the potential of forming the basis of novel devices in spintronics and quantum computing. While exposure to ambient conditions and conventional fabrication processes are an obstacle to their technological integration, ultra-high vacuum lithography techniques, such as selective area epitaxy (SAE), provide all the necessary ingredients for their refinement into scalable device architectures. In this work, high-quality SAE of quasi-1D topological insulators on templated Si substrates is demonstrated. After identifying the narrow temperature window for selectivity, the flexibility and scalability of this approach is revealed. Compared to planar growth of macroscopic thin films, selectively grown regions are observed to experience enhanced growth rates in the nanostructured templates. Based on these results, a growth model is deduced, which relates device geometry to effective growth rates. After validating the model experimentally for various three-dimensional topological insulators (3D TIs), the crystal quality of selectively grown nanostructures is optimized by tuning the effective growth rates to 5 nm/h. The high quality of selectively grown nanostructures is confirmed through detailed structural characterization via atomically resolved scanning transmission electron microscopy (STEM).

Competing Vortex Topologies in Iron-Based Superconductors

In this Letter, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (TFeSCs). While TFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic s-wave superconductivity, our theory implies that such a common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for TFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in TFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for TFeSCs and is directly relevant to TFeSC candidates such as LiFeAs. When the fourfold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. The origin of the Majorana signal in other TFeSC candidates such as FeTe_{x}Se_{1-x} and CaKFe_{4}As_{4} is also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems.

Selective control of conductance modes in multi-terminal Josephson junctions

The Andreev bound state spectra of multi-terminal Josephson junctions form an artificial band structure, which is predicted to host tunable topological phases under certain conditions. However, the number of conductance modes between the terminals of a multi-terminal Josephson junction must be few in order for this spectrum to be experimentally accessible. In this work, we employ a quantum point contact geometry in three-terminal Josephson devices to demonstrate independent control of conductance modes between each pair of terminals and access to the single-mode regime coexistent with the presence of superconducting coupling. These results establish a full platform on which to realize tunable Andreev bound state spectra in multi-terminal Josephson junctions.

Multiterminal Josephson junctions may provide a novel way to realize topologically non-trivial band structures in an n-dimensional phase space. Here, the authors experimentally demonstrate the proposed necessary conditions to measure these states.

Proximity-Effect-Induced Anisotropic Superconductivity in a Monolayer Ni-Pb Binary Alloy

A proximity effect facilitates the penetration of Cooper pairs that permits superconductivity in a normal metal, offering a promising approach to turn heterogeneous materials into superconductors and develop exceptional quantum phenomena. Here, we have systematically investigated proximity-induced anisotropic superconductivity in a monolayer Ni-Pb binary alloy by combining scanning tunneling microscopy/spectroscopy (STM/STS) with theoretical calculations. By means of high-temperature growth, the ( 3 3 × 3 3 ) R 30 o Ni-Pb surface alloy has been fabricated on Pb(111) and the appearance of a domain boundary as well as a structural phase transition can be deduced from a half-unit-cell lattice displacement. Given the high spatial and energy resolution, tunneling conductance (dI/dU) spectra have resolved the reduced but anisotropic superconducting gap ΔNiPb ≈ 1.0 meV, in stark contrast to the isotropic ΔPb ≈ 1.3 meV. In addition, the higher density of states at the Fermi energy (D(EF)) of the Ni-Pb surface alloy results in an enhancement of coherence peak height. According to the same Tc ≈ 7.1 K with Pb(111) from the temperature-dependent ΔNiPb and the short decay length Ld ≈ 3.55 nm from the spatially monotonic decrease of ΔNiPb, both results are supportive of a proximity-induced superconductivity. Despite a lack of a bulk counterpart, the atomically thick Ni-Pb bimetallic compound opens a pathway to engineer superconducting properties down to the two-dimensional limit, giving rise to the emergence of anisotropic superconductivity via a proximity effect.

Local Control of Supercurrent Density in Epitaxial Planar Josephson Junctions

The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density, and therefore the overall current distribution, can be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five minigates. We demonstrate that not only can the junction width be electrostatically defined but also the current profile can be locally adjusted to form superconducting quantum interference devices. Our studies show enhanced edge conduction in such long junctions, which can be eliminated by minigates to create a uniform current distribution.

Quantized critical supercurrent in SrTiO3-based quantum point contacts

Superconductivity in SrTiO3 occurs at remarkably low carrier densities and therefore, unlike conventional superconductors, can be controlled by electrostatic gates. Here, we demonstrate nanoscale weak links connecting superconducting leads, all within a single material, SrTiO3. Ionic liquid gating accumulates carriers in the leads, and local electrostatic gates are tuned to open the weak link. These devices behave as superconducting quantum point contacts with a quantized critical supercurrent. This is a milestone toward establishing SrTiO3 as a single-material platform for mesoscopic superconducting transport experiments that also intrinsically contains the necessary ingredients to engineer topological superconductivity.

Hybrid Symmetry Epitaxy of the Superconducting Fe(Te,Se) Film on a Topological Insulator

It is challenging to grow an epitaxial 4-fold compound superconductor (SC) on a 6-fold topological insulator (TI) platform due to the stringent lattice-matching requirement. Here, we demonstrate that Fe(Te,Se) can grow epitaxially on a TI (Bi2Te3) layer due to accidental, uniaxial lattice match, which is dubbed as "hybrid symmetry epitaxy". This new growth mode is critical to stabilizing robust superconductivity with TC as high as 13 K. Furthermore, the superconductivity in this FeTe1-xSex/Bi2Te3 system survives in the Te-rich phase with Se content as low as x = 0.03 but vanishes at Se content above x = 0.56, exhibiting a phase diagram that is quite different from that of the conventional Fe(Te,Se) systems. This unique heterostructure platform that can be formed in both TI-on-SC and SC-on-TI sequences opens a route to unprecedented topological heterostructures.

Asymmetric Fraunhofer spectra in a topological insulator-based Josephson junction

Josephson junctions with topological insulators as their weak link (S-TI-S junctions) are predicted to host Majorana fermions, which are key to creating qubits for topologically protected quantum computing. But the details of the S-TI-S current-phase relation and its interplay with magnetic fields are not well understood. We fabricate a Bi₂Se₃junction with NbTi leads and measure the Fraunhofer patterns of the junction with applied in-plane fields. We observe that asymmetric Fraunhofer patterns appear in the resistance maps ofB_zvsB_x,y, with aperiodic node spacings. These asymmetric patterns appear even at zero parallel field and for temperatures up to 1 K. The anomalous features are compared to asymmetric Fraunhofer patterns expected for finite Cooper pair momentum shifts as well as geometric effects. We show that the geometric effects can dominate, independent of in-plane field magnitude. These results are important for differentiating geometrical phase shifts from those caused by Cooper pair momentum shifting, Majorana mode signatures, or other unconventional superconducting behavior.

Nonadiabatic charge pumping across two superconductors connected through a normal metal region by periodically driven potentials

Periodically driven systems exhibit resonance when the difference between an excited state energy and the ground state energy is an integer multiple ofℏtimes the driving frequency. On the other hand, when a superconducting phase difference is maintained between two superconductors, subgap states appear which carry a Josephson current. A driven Josephson junction therefore opens up an interesting avenue where the excitations due to applied driving affect the current flowing from one superconductor to the other. Motivated by this, we study charge transport in a superconductor-normal metal-superconductor junction where oscillating potentials are applied to the normal metal region. We find that for small amplitudes of the oscillating potential, driving at one site reverses the direction of current at the superconducting phase differences when difference between the subgap eigenenergies of the undriven Hamiltonian is integer multiple ofℏtimes the driving frequency. For larger amplitudes of oscillating potential, driving at one site exhibits richer features. We show that even when the two superconductors are maintained at same superconducting phase, a current can be driven by applying oscillating potentials to two sites in the normal metal differing by a phase. We find that when there is a nonzero Josephson current in the undriven system, the local peaks and valleys in current of the system driven with an amplitude of oscillating potential smaller than the superconducting gap indicates sharp excitations in the system. In the adiabatic limit, we find that charge transferred in one time period diverges as a powerlaw with pumping frequency when a Josephson current flows in the undriven system. Our calculations are exact and can be applied to finite systems. We discuss possible experimental setups where our predictions can be tested.

Massive Suppression of Proximity Pairing in Topological (Bi_{1-x}Sb_{x})_{2}Te_{3} Films on Niobium

Interfacing bulk conducting topological Bi_{2}Se_{3} films with s-wave superconductors initiates strong superconducting order in the nontrivial surface states. However, bulk insulating topological (Bi_{1-x}Sb_{x})_{2}Te_{3} films on bulk Nb instead exhibit a giant attenuation of surface superconductivity, even for films only two layers thick. This massive suppression of proximity pairing is evidenced by ultrahigh-resolution band mappings and by contrasting quantified superconducting gaps with those of heavily n-doped topological Bi_{2}Se_{3}/Nb. The results underscore the limitations of using superconducting proximity effects to realize topological superconductivity in nearly intrinsic systems.

Development of topological insulator and topological crystalline insulator nanostructures

Topological insulators (TIs), a class of quantum materials with time reversal symmetry protected gapless Dirac-surface states, have attracted intensive research interests due to their exotic electronic properties. Topological crystalline insulators (TCIs), whose gapless surface states are protected by the crystal symmetry, have recently been proposed and experimentally verified as a new class of TIs. With high surface-to-volume ratio, nanoscale TI and TCI materials such as nanowires and nanoribbons can have significantly enhanced contribution from surface states in carrier transport and are thus ideally suited for the fundamental studies of topologically protected surface state transport and nanodevice fabrication. This article will review the synthesis and transport device measurements of TIs and TCIs nanostructures.

Signature of a pair of Majorana zero modes in superconducting gold surface states

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin-orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.

Probing the magnetoelectric effect in noncentrosymmetric superconductors by equal-spin Andreev tunneling

In noncentrosymmetric superconductors (NCSs), the conversion of a charge current into spin magnetization-the so called magnetoelectric effect-is the direct indicator of the unconventional, mixed-parity order parameter. This paper proposes a scheme to detect the magnetoelectric effect by anomalous, equal-spin Andreev tunneling in NCS/ferromagnet contacts. The proposal relies on the ability to generate spin-polarized triplet pairing by passing an electric current through an NCS. Such an induced triplet pairing bears a similarity to the paradigmatic nonunitary pairing in triplet superfluids with a complex vector order parameter [Formula: see text]. The qualitative difference is that the induced nonunitary state can be realised in NCSs with a purely real [Formula: see text] by breaking the time-reversal symmetry in current-biased setups. This offers a possibility to access the unconventional superconductivity in NCSs through electrical transport measurements.

Anomalous Low-Temperature Enhancement of Supercurrent in Topological-Insulator Nanoribbon Josephson Junctions: Evidence for Low-Energy Andreev Bound States

We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator BiSbTeSe_{2} nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a function of the decreasing temperature T, the increasing critical current I_{c} exhibits a sharp upturn at a temperature T_{*} around 20% of the junction critical temperature for several different samples and various gate voltages. The I_{c} vs T demonstrates a short junction behavior for T>T_{*}, but crosses over to a long junction behavior for T<T_{*} with an exponential T dependence I_{c}∝exp(-k_{B}T/δ), where k_{B} is the Boltzmann constant. The extracted characteristic energy scale δ is found to be an order of magnitude smaller than the induced superconducting gap of the junction. We attribute the long-junction behavior with such a small δ to low-energy Andreev bound states arising from winding of the electronic wave function around the circumference of the topological insulator nanoribbon.

Conductance Spectroscopy of Exfoliated Thin Flakes of Nb xBi2Se3

We study unconventional superconductivity in exfoliated single crystals of a promising three-dimensional (3D) topological superconductor candidate, Nb-doped Bi₂Se₃ through differential conductance spectroscopy and magneto-transport. The strong anisotropy of the critical field along the out-of-plane direction suggests that the thin exfoliated flakes are in the quasi-2D limit. Normal metal-superconductor (NS) contacts with either high or low transparencies made by depositing gold leads onto Nb-doped Bi₂Se₃ flakes both show significant enhancement in zero bias conductance and coherence dips at the superconducting energy gap. Such behavior is inconsistent with conventional Blonder-Tinkham-Klapwijk theory. Instead, we discuss how our results are consistent with p-wave pairing symmetry, supporting the possibility of topological superconductivity in Nb-doped Bi₂Se₃. Finally, we observe signatures of multiple superconducting energy gaps, which could originate from multiple Fermi surfaces reported earlier in bulk crystals.

Signatures of Topological Superconductivity in Bulk-Insulating Topological Insulator BiSbTe1.25Se1.75 in Proximity with Superconducting NbSe2

The combination of superconductivity and spin-momentum locking at the interface between an s-wave superconductor and a three-dimensional topological insulator (3D-TI) is predicted to generate exotic p-wave topological superconducting phases that can host Majorana Fermions. However, large bulk conductivities of previously investigated 3D-TI samples and Fermi level mismatches between 3D bulk superconductors and 2D topological surface states have thwarted significant progress. Here, we employ bulk-insulating topological insulators in proximity with two-dimensional superconductor NbSe₂ assembled via van der Waals epitaxy. Experimentally measured differential conductance yields unusual features including a double-gap spectrum, an intrinsic asymmetry that vanishes with small in-plane magnetic fields, and differential conductance ripples at biases significantly larger than the superconducting gap. We explain our results on the basis of proximity-induced superconductivity of topological surface states, while also considering possibilities of topologically trivial superconductivity arising from Rashba-type surface states. Our work demonstrates the possibility of obtaining p-wave superconductors by proximity effects on bulk-insulating TIs.

Proximity-induced supercurrent through topological insulator based nanowires for quantum computation studies

Proximity-induced superconducting energy gap in the surface states of topological insulators has been predicted to host the much wanted Majorana fermions for fault-tolerant quantum computation. Recent theoretically proposed architectures for topological quantum computation via Majoranas are based on large networks of Kitaev’s one-dimensional quantum wires, which pose a huge experimental challenge in terms of scalability of the current single nanowire based devices. Here, we address this problem by realizing robust superconductivity in junctions of fabricated topological insulator (Bi₂Se₃) nanowires proximity-coupled to conventional s-wave superconducting (W) electrodes. Milling technique possesses great potential in fabrication of any desired shapes and structures at nanoscale level, and therefore can be effectively utilized to scale-up the existing single nanowire based design into nanowire based network architectures. We demonstrate the dominant role of ballistic topological surface states in propagating the long-range proximity induced superconducting order with high I_cR_N product in long Bi₂Se₃ junctions. Large upper critical magnetic fields exceeding the Chandrasekhar-Clogston limit suggests the existence of robust superconducting order with spin-triplet cooper pairing. An unconventional inverse dependence of I_cR_N product on the width of the nanowire junction was also observed.

Weak-link Josephson Junctions Made from Topological Crystalline Insulators

We report on the fabrication of Josephson junctions using the topological crystalline insulator Pb_{0.5}Sn_{0.5}Te as the weak link. The properties of these junctions are characterized and compared to those fabricated with weak links of PbTe, a similar material yet topologically trivial. Most striking is the difference in the ac Josephson effect: junctions made with Pb_{0.5}Sn_{0.5}Te exhibit a rich subharmonic structure consistent with a skewed current-phase relation. This structure is absent in junctions fabricated from PbTe. A discussion is given on the origin of this effect as an indication of novel behavior arising from the topologically nontrivial surface state.

Anomalous Fraunhofer Patterns in Gated Josephson Junctions Based on the Bulk-Insulating Topological Insulator BiSbTeSe2

One-dimensional Majorana modes are predicated to form in Josephson junctions based on three-dimensional topological insulators (TIs). While observations of supercurrents in Josephson junctions made on bulk-insulating TI samples have been reported recently, the Fraunhofer patters observed in such TI-based Josephson junctions, which sometimes present anomalous features, are still not well-understood. Here, we report our study of highly gate-tunable TI-based Josephson junctions made of one of the most bulk-insulating TI materials, BiSbTeSe₂, and Al. The Fermi level can be tuned by gating across the Dirac point, and the high transparency of the Al-BiSbTeSe₂ interface is evinced by a high characteristic voltage and multiple Andreev reflections, with peak indices reaching 12. Anomalous Fraunhofer patterns with missing lobes were observed in the entire range of gate voltage. We found that, by employing an advanced fitting procedure to use the maximum entropy method in a Monte Carlo algorithm, the anomalous Fraunhofer patterns are explained as a result of inhomogeneous supercurrent distributions on the TI surface in the junction. Besides establishing a highly promising fabrication technology, this work clarifies one of the important open issues regarding TI-based Josephson junctions.

Onset of a Two-Dimensional Superconducting Phase in a Topological-Insulator-Normal-Metal Bi_{1-x}Sb_{x}/Pt Junction Fabricated by Ion-Beam Techniques

Inducing superconductivity in a topological insulator can lead to novel quantum effects. However, experimental approaches to turn a topological insulator into a superconductor are limited. Here, we report on superconductivity in topological insulator Bi_{0.91}Sb_{0.09} induced via focused ion-beam deposition of a Pt thin film. The superconducting phase exhibits a Berezinski-Kosterlitz-Thouless transition, demonstrative of its two-dimensional character. From the in-plane upper critical field measurements, we estimate the superconducting thickness to be ∼17  nm for a 5.5-μm-thick sample. Our results provide evidence that the interface superconductivity could originate from the surface states of Bi_{0.91}Sb_{0.09}.

Topological π Junctions from Crossed Andreev Reflection in the Quantum Hall Regime

We consider a two-dimensional electron gas (2DEG) in the quantum Hall regime in the presence of a Zeeman field, with the Fermi level tuned to a filling factor of ν=1. We show that, in the presence of spin-orbit coupling, contacting the 2DEG with a narrow strip of an s-wave superconductor produces a topological superconducting gap along the contact as a result of crossed Andreev reflection (CAR) processes across the strip. The sign of the topological gap, controlled by the CAR amplitude, depends periodically on the Fermi wavelength and strip width and can be externally tuned. An interface between two halves of a long strip with topological gaps of opposite sign implements a robust π junction, hosting a pair of Majorana zero modes that do not split despite their overlap. We show that such a configuration can be exploited to perform protected non-Abelian tunnel-braid operations without any fine tuning.

Creation of Spin-Triplet Cooper Pairs in the Absence of Magnetic Ordering

In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction-the Dirac surface states of a strong topological insulator (TI)-out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin-triplet filter across the SC, generating equal-spin Cooper pairs via crossed Andreev reflection.

Induced unconventional superconductivity on the surface states of Bi2Te3 topological insulator

Topological superconductivity is central to a variety of novel phenomena involving the interplay between topologically ordered phases and broken-symmetry states. The key ingredient is an unconventional order parameter, with an orbital component containing a chiral p x  + ip y wave term. Here we present phase-sensitive measurements, based on the quantum interference in nanoscale Josephson junctions, realized by using Bi2Te3 topological insulator. We demonstrate that the induced superconductivity is unconventional and consistent with a sign-changing order parameter, such as a chiral p x  + ip y component. The magnetic field pattern of the junctions shows a dip at zero externally applied magnetic field, which is an incontrovertible signature of the simultaneous existence of 0 and π coupling within the junction, inherent to a non trivial order parameter phase. The nano-textured morphology of the Bi2Te3 flakes, and the dramatic role played by thermal strain are the surprising key factors for the display of an unconventional induced order parameter.

Thermal transport in topological-insulator-based superconducting hybrid structures with mixed singlet and triplet pairing states

In the framework of the Bogoliubov-de Gennes equation, we investigate the thermal transport properties in topological-insulator-based superconducting hybrid structures with mixed spin-singlet and spin-triplet pairing states, and emphasize the different manifestations of the spin-singlet and spin-triplet pairing states in the thermal transport signatures. It is revealed that the temperature-dependent differential thermal conductance strongly depends on the components of the pairing state, and the negative differential thermal conductance only occurs in the spin-singlet pairing state dominated regime. It is also found that the thermal conductance is profoundly sensitive to the components of the pairing state. In the spin-singlet pairing state controlled regime, the thermal conductance obviously oscillates with the phase difference and junction length. With increasing the proportion of the spin-triplet pairing state, the oscillating characteristic of the thermal conductance fades out distinctly. These results suggest an alternative route for distinguishing the components of pairing states in topological-insulator-based superconducting hybrid structures.

Macroscopic Quantum Tunneling in Superconducting Junctions of β-Ag2Se Topological Insulator Nanowire

We report on the fabrication and electrical transport properties of superconducting junctions made of β-Ag₂Se topological insulator (TI) nanowires in contact with Al superconducting electrodes. The temperature dependence of the critical current indicates that the superconducting junction belongs to a short and diffusive junction regime. As a characteristic feature of the narrow junction, the critical current decreases monotonously with increasing magnetic field. The stochastic distribution of the switching current exhibits the macroscopic quantum tunneling behavior, which is robust up to T = 0.8 K. Our observations indicate that the TI nanowire-based Josephson junctions can be a promising building block for the development of nanohybrid superconducting quantum bits.

Effect of random feld disorder on topological superconductors

We study the effect of random field disorder on two dimensional topological superconductors based on the Bogoliubov-de Gennes equations. A phase transition from the phase coherent state to the disordered state is identified numerically. The two phases can be characterized by two different correlation functions. In the phase coherent state, Majorana Fermion states form and may be influenced by the interaction between the vortex and the antivortex. The local density of states is calculated, which may be used to distinguish these two phases.

Proximity-effect-induced Superconducting Gap in Topological Surface States - A Point Contact Spectroscopy Study of NbSe2/Bi2Se3 Superconductor-Topological Insulator Heterostructures

Proximity-effect-induced superconductivity was studied in epitaxial topological insulator Bi2Se3 thin films grown on superconducting NbSe2 single crystals. A point contact spectroscopy (PCS) method was used at low temperatures down to 40 mK. An induced superconducting gap in Bi2Se3 was observed in the spectra, which decreased with increasing Bi2Se3 layer thickness, consistent with the proximity effect in the bulk states of Bi2Se3 induced by NbSe2. At very low temperatures, an extra point contact feature which may correspond to a second energy gap appeared in the spectrum. For a 16 quintuple layer Bi2Se3 on NbSe2 sample, the bulk state gap value near the top surface is ~159 μeV, while the second gap value is ~120 μeV at 40 mK. The second gap value decreased with increasing Bi2Se3 layer thickness, but the ratio between the second gap and the bulk state gap remained about the same for different Bi2Se3 thicknesses. It is plausible that this is due to superconductivity in Bi2Se3 topological surface states induced through the bulk states. The two induced gaps in the PCS measurement are consistent with the three-dimensional bulk state and the two-dimensional surface state superconducting gaps observed in the angle-resolved photoemission spectroscopy (ARPES) measurement.

Topological superconductors: a review

This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

Patterning Superconductivity in a Topological Insulator

Topologically protected states in combination with superconductivity hold great promise for quantum computing applications, but the progress on electrical transport measurements in such systems has been impeded by the difficulty of fabricating devices with reliable electrical contacts. We find that superconductivity can be patterned directly into Bi₂Se₃ nanostructures by local doping with palladium. Superconducting regions are defined by depositing palladium on top of the nanostructures using electron beam lithography followed by in situ annealing. Electrical transport measurements at low temperatures show either partial or full superconducting transition, depending on the doping conditions. Structural characterization techniques indicate that palladium remains localized in the targeted areas, making it possible to pattern superconducting circuits of arbitrary shapes in this topological material.

Inducing superconductivity in Weyl semimetal microstructures by selective ion sputtering

By introducing a superconducting gap in Weyl or Dirac semimetals, the superconducting state inherits the nontrivial topology of their electronic structure. As a result, Weyl superconductors are expected to host exotic phenomena, such as nonzero-momentum pairing due to their chiral node structure, or zero-energy Majorana modes at the surface. These are of fundamental interest to improve our understanding of correlated topological systems, and, moreover, practical applications in phase-coherent devices and quantum applications have been proposed. Proximity-induced superconductivity promises to allow these experiments on nonsuperconducting Weyl semimetals. We show a new route to reliably fabricate superconducting microstructures from the nonsuperconducting Weyl semimetal NbAs under ion irradiation. The significant difference in the surface binding energy of Nb and As leads to a natural enrichment of Nb at the surface during ion milling, forming a superconducting surface layer (T_c ~ 3.5 K). Being formed from the target crystal itself, the ideal contact between the superconductor and the bulk may enable an effective gapping of the Weyl nodes in the bulk because of the proximity effect. Simple ion irradiation may thus serve as a powerful tool for the fabrication of topological quantum devices from monoarsenides, even on an industrial scale.

Magnetically-driven colossal supercurrent enhancement in InAs nanowire Josephson junctions

The Josephson effect is a fundamental quantum phenomenon where a dissipationless supercurrent is introduced in a weak link between two superconducting electrodes by Andreev reflections. The physical details and topology of the junction drastically modify the properties of the supercurrent and a strong enhancement of the critical supercurrent is expected to occur when the topology of the junction allows an emergence of Majorana bound states. Here we report charge transport measurements in mesoscopic Josephson junctions formed by InAs nanowires and Ti/Al superconducting leads. Our main observation is a colossal enhancement of the critical supercurrent induced by an external magnetic field applied perpendicular to the substrate. This striking and anomalous supercurrent enhancement cannot be described by any known conventional phenomenon of Josephson junctions. We consider these results in the context of topological superconductivity, and show that the observed critical supercurrent enhancement is compatible with a magnetic field-induced topological transition.

Physical details of a Josephson junction may drastically modify the properties of supercurrent. Here, the authors observe a colossal enhancement of the critical supercurrent in a Josephson junction subject to a perpendicular magnetic field, indicating topological phase transitions.

Hard Superconducting Gap in InSb Nanowires

Topological superconductivity is a state of matter that can host Majorana modes, the building blocks of a topological quantum computer. Many experimental platforms predicted to show such a topological state rely on proximity-induced superconductivity. However, accessing the topological properties requires an induced hard superconducting gap, which is challenging to achieve for most material systems. We have systematically studied how the interface between an InSb semiconductor nanowire and a NbTiN superconductor affects the induced superconducting properties. Step by step, we improve the homogeneity of the interface while ensuring a barrier-free electrical contact to the superconductor and obtain a hard gap in the InSb nanowire. The magnetic field stability of NbTiN allows the InSb nanowire to maintain a hard gap and a supercurrent in the presence of magnetic fields (∼0.5 T), a requirement for topological superconductivity in one-dimensional systems. Our study provides a guideline to induce superconductivity in various experimental platforms such as semiconductor nanowires, two-dimensional electron gases, and topological insulators and holds relevance for topological superconductivity and quantum computation.

Topological superconductivity in monolayer transition metal dichalcogenides

Theoretically, it has been known that breaking spin degeneracy and effectively realizing spinless fermions is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here we propose to realize spinless fermions by splitting the spin degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological because of the near spin degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favours two topological superconducting states: interpocket paired state with Chern number 2 and intrapocket paired state with finite pair momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device-friendly platform of monolayer TMDs.

Two-Dimensional Platform for Networks of Majorana Bound States

We model theoretically a two-dimensional electron gas (2DEG) covered by a superconductor and demonstrate that topological superconducting channels are formed when stripes of the superconducting layer are removed. As a consequence, Majorana bound states (MBSs) are created at the ends of the stripes. We calculate the topological invariant and energy gap of a single stripe, using realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We show that the topological gap is enhanced when the structure is made asymmetric. This can be achieved either by imposing a phase difference (by driving a supercurrent or using a magnetic-flux loop) over the strip or by replacing one superconductor by a metallic gate. Both strategies also enable control over the MBS splitting, thereby facilitating braiding and readout schemes based on controlled fusion of MBSs. Finally, we outline how a network of Majorana stripes can be designed.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

All Majorana Models with Translation Symmetry are Supersymmetric

We establish results similar to Kramers and Lieb-Schultz-Mattis theorems but involving only translation symmetry and for Majorana modes. In particular, we show that all states are at least doubly degenerate in any one- and two-dimensional array of Majorana modes with translation symmetry, periodic boundary conditions, and an odd number of modes per unit cell. Moreover, we show that all such systems have an underlying N=2 supersymmetry and explicitly construct the generator of the supersymmetry. Furthermore, we establish that there cannot be a unique gapped ground state in such one-dimensional systems with antiperiodic boundary conditions. These general results are fundamentally a consequence of the fact that translations for Majorana modes are represented projectively, which in turn stems from the anomalous nature of a single Majorana mode. An experimental signature of the degeneracy arising from supersymmetry is a zero-bias peak in tunneling conductance.

Andreev Reflection in an s-Type Superconductor Proximized 3D Topological Insulator

We investigate transport and shot noise in lateral normal-metal-3D topological-insulator-superconductor contacts, where the 3D topological insulator (TI) is based on Bi. In the normal state, the devices are in the elastic diffusive transport regime, as demonstrated by a nearly universal value of the shot noise Fano factor F_{N}≈1/3 in magnetic field and in a reference normal-metal contact. In the absence of magnetic field, we identify the Andreev reflection (AR) regime, which gives rise to the effective charge doubling in shot noise measurements. Surprisingly, the Fano factor F_{AR}≈0.22±0.02 is considerably reduced in the AR regime compared to F_{N}, in contrast to previous AR experiments in normal metals and semiconductors. We suggest that this effect is related to a finite thermal conduction of the proximized, superconducting TI owing to a residual density of states at low energies.

Robust two-dimensional superconductivity and vortex system in Bi2Te3/FeTe heterostructures

The discovery of two-dimensional superconductivity in Bi2Te3/FeTe heterostructures provides a new platform for the search of Majorana fermions in condensed matter systems. Since Majorana fermions are expected to reside at the core of the vortices, a close examination of the vortex dynamics in superconducting interface is of paramount importance. Here, we report the robustness of the interfacial superconductivity and 2D vortex dynamics in four as-grown and aged Bi2Te3/FeTe heterostructure with different Bi2Te3 epilayer thickness (3, 5, 7, 14 nm). After two years' air exposure, superconductivity remains robust even when the thickness of Bi2Te3 epilayer is down to 3 nm. Meanwhile, a new feature at ~13 K is induced in the aged samples, and the high field studies reveal its relevance to superconductivity. The resistance of all as-grown and aged heterostructures, just below the superconducting transition temperature follows the Arrhenius relation, indicating the thermally activated flux flow behavior at the interface of Bi2Te3 and FeTe. Moreover, the activation energy exhibits a logarithmic dependence on the magnetic field, providing a compelling evidence for the 2D vortex dynamics in this novel system. The weak disorder associated with aging-induced Te vacancies is possibly responsible for these observed phenomena.

Topological Floquet Phases in Driven Coupled Rashba Nanowires

We consider periodically driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This nonequilibrium system can be tuned into nontrivial phases such as topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges e/m with m being an odd integer.

Globally symmetric topological phase: from anyonic symmetry to twist defect

Topological phases in two dimensions support anyonic quasiparticle excitations that obey neither bosonic nor fermionic statistics. These anyon structures often carry global symmetries that relate distinct anyons with similar fusion and statistical properties. Anyonic symmetries associate topological defects or fluxes in topological phases. As the symmetries are global and static, these extrinsic defects are semiclassical objects that behave disparately from conventional quantum anyons. Remarkably, even when the topological states supporting them are Abelian, they are generically non-Abelian and powerful enough for topological quantum computation. In this article, I review the most recent theoretical developments on symmetries and defects in topological phases.

Bulk Topological Proximity Effect

Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases also may give rise to a proximity effect of a distinctively inverted nature. We focus on a general construction in which a topological phase is extensively coupled to a second system, and we argue that, in many cases, the inverse topological order will be induced on the second system. To support our arguments, we rigorously establish this "bulk topological proximity effect" for all gapped free-fermion topological phases and representative integrable models of interacting topological phases. We present a terrace construction which illustrates the phenomenological consequences of this proximity effect. Finally, we discuss generalizations beyond our framework, including how intrinsic topological order may also exhibit this effect.

Dirac fermions at high-index surfaces of bismuth chalcogenide topological insulator nanostructures

Binary bismuth chalcogenides Bi₂Se₃, Bi₂Te₃, and related materials are currently being extensively investigated as the reference topological insulators (TIs) due to their simple surface-state band dispersion (single Dirac cone) and relatively large bulk band gaps. Nanostructures of TIs are of particular interest as an increased surface-to-volume ratio enhances the contribution of surfaces states, meaning they are promising candidates for potential device applications. So far, the vast majority of research efforts have focused on the low-energy (0001) surfaces, which correspond to natural cleavage planes in these layered materials. However, the surfaces of low-dimensional nanostructures (nanoplatelets, nanowires, nanoribbons) inevitably involve higher-index facets. We perform a systematic ab initio investigation of the surfaces of bismuth chalcogenide TI nanostructures characterized by different crystallographic orientations, atomic structures and stoichiometric compositions. We find several stable terminations of high-index surfaces, which can be realized at different values of the chemical potential of one of the constituent elements. For the uniquely defined stoichiometric termination, the topological Dirac fermion states are shown to be strongly anisotropic with a clear dependence of Fermi velocities and spin polarization on the surface orientation. Self-doping effects and the presence of topologically trivial mid-gap states are found to characterize the non-stoichiometric surfaces. The results of our study pave the way towards experimental control of topologically protected surface states in bismuth chalcogenide nanostructures.

Effect of Impurities on the Josephson Current through Helical Metals: Exploiting a Neutrino Paradigm

In this Letter we study the effect of time-reversal symmetric impurities on the Josephson supercurrent through two-dimensional helical metals such as on a topological insulator surface state. We show that, contrary to the usual superconducting-normal metal-superconducting junctions, the suppression of the supercurrent in the superconducting-helical metal-superconducting junction is mainly due to fluctuations of impurities in the junctions. Our results, which are a condensed matter realization of a part of the Mikheyev-Smirnov-Wolfenstein effect for neutrinos, show that the relationship between normal state conductance and the critical current of Josephson junctions is significantly modified for Josephson junctions on the surface of topological insulators. We also study the temperature dependence of the supercurrent and present a two fluid model which can explain some of the recent experimental results in Josephson junctions on the edge of topological insulators.

Detecting the Exchange Phase of Majorana Bound States in a Corbino Geometry Topological Josephson Junction

A phase from an adiabatic exchange of Majorana bound states (MBS) reveals their exotic anyonic nature. For detecting this exchange phase, we propose an experimental setup consisting of a Corbino geometry Josephson junction on the surface of a topological insulator, in which two MBS at zero energy can be created and rotated. We find that if a metallic tip is weakly coupled to a point on the junction, the time-averaged differential conductance of the tip-Majorana coupling shows peaks at the tip voltages eV=±(α-2πl)ℏ/T_{J}, where α=π/2 is the exchange phase of the two circulating MBS, T_{J} is the half rotation time of MBS, and l an integer. This result constitutes a clear experimental signature of Majorana fermion exchange.

Surface Plasmon Enhanced Sensitive Detection for Possible Signature of Majorana Fermions via a Hybrid Semiconductor Quantum Dot-Metal Nanoparticle System

In the present work, we theoretically propose an optical scheme to detect the possible signature of Majorana fermions via the optical pump-probe spectroscopy, which is very different from the current tunneling measurement based on electrical methods. The scheme consists of a metal nanoparticle and a semiconductor quantum dot coupled to a hybrid semiconductor/superconductor heterostructures. The results show that the probe absorption spectrum of the quantum dot presents a distinct splitting due to the existence of Majorana fermions. Owing to surface plasmon enhanced effect, this splitting will be more obvious, which makes Majorana fermions more easy to be detectable. The technique proposed here open the door for new applications ranging from robust manipulation of Majorana fermions to quantum information processing based on Majorana fermions.